ADC

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To calculate an apparent diffusion coefficient (ADC) map based on diffusion weighted images, at least two volumes with different b-values are required. An optional mask can also be provided to limit the calculations to a region of interest.

Two methods can be used for the calculation of the ADC map: a linear (fast) method and a nonlinear (slower) method. Both methods typically produce good results, but the linear method involves taking the logarithm of a signal before fitting parameters and may not treat noise optimally. Therefore, for lower signal-to-noise ratio data, the nonlinear method is preferred.

The estimation is based on a signal equation

\[ S_i = S_0 \exp(-b_i \cdot ADC), i=0,1,2,\ldots. n \]

where \(i\) is an index over \(n\) images acquired with different b-values.

The unit of the ADC map in determined by the unit of the b-values. A common b-value unit used in most MRI scanners and in DICOM tags are \(\textrm{s}/\textrm{mm}^2\), and common b-values are in the range [0, 2000]. This gives the unit of the ADC map in \(\textrm{mm}^2/\textrm{s}\). This is usually multiplied by a factor of 1e6 to give ADC values in approximate range [0, 3500].

Another common unit for b-values is \(\textrm{ms}/\mu\textrm{m}^2\), and common b-values are in the range [0, 2]. This gives the unit of the ADC map in \(\mu\textrm{m}^2/\textrm{ms}\), and ADC values are in the approximate range [0, 3.5]. One benefit of these values are that they don't require scaling to be easily readable without scientific notification.

Inputs

Dataset

Input diffusion weighted dataset. Different b-values must be found in one or more channels of the dataset.

Type: Image, Required, Single

Mask

A 3D binary mask defining the region in the image where the ADC map is calculated.

Type: Mask, Optional, Single

Outputs

ADC

ADC map.

Type: Image

S0

The signal with no diffusion weighting.

Type: Image

Settings

Configure

Algorithm Selection

Use a linearized or a nonlinear fitting model. When selecting a nonlinear model, equation (1) is fit directly with a square loss term. In the linearized case the data is transformed using a logarithm to yield a linear system of equations: \(\ln{S_i} = \ln{S_0} - b_i \cdot ADC, i=0,1,2,\ldots, n\). The ADC values and \(S_0\) are obtained using linear regression.

Values: Linear, NonLinear

Batch Size Integer

The number of voxels that are computed per batch. This is a trade-off between performance and memory consumption.

Keep Metadata Boolean

Keep or discard metadata in the parameter maps.

Metadata

B-values Source Selection

Select the b-value source for the calculation. The b-values can be taken from the metadata, or can be supplied as an input Numeric Array.

Values: Metadata, Numeric Array Input

B-value Tag Text

The B-value tag name in the metadata.

Configure NonLinear

Tolerance Float

The threshold change in the objective function. Changes smaller than this value imply that the fitting has converged.

Max Iterations Integer

Maximum number of iterations.

Return Convergence Map Boolean

Return a binary mask, where all true voxels have converged in the fit. This can be used to exclude voxels that did not converge.

ADC